On the Floquet Theory of Delay Differential Equations

We present an analytical approach to deal with nonlinear delay differential equations close to instabilities of time periodic reference states. To this end we start with approximately determining such reference states by extending the Poincar'e Lindstedt and the Shohat expansions which were originally developed for ordinary differential equations. Then we systematically elaborate a linear stability analysis around a time periodic reference state. This allows to approximately calculate the Floquet eigenvalues and their corresponding eigensolutions by using matrix valued continued fractions

Synthesis, stability and zeolitic behavior of δ­ALn3F10,xH2O and γ­ThLn2F10,H2O phases (Ln = lanthanide)

Two series of hydrated fluorides have been prepared by a “chimie douce” process. For the first family, more than twenty five compounds of δ-ALn3F10,xH2O (A+ = alkaline ions, NH4+, H3O+ and Ln = lanthanide) have been prepared. They crystallize in the Fd [[3 with combining macron]] m space group (a ≈ 15.4 Å and Z = 16) and are isotypic with δ-(H3O)Yb3F10,xH2O (x = 1). The diamond-type structure of these phases (diamond stacking of octahedral units of antiprisms, called UOA[8]), creates cavities and tunnels where the water molecules can move. The second family, γ-ThLn2F10,H2O (Ln3+ = Er3+, Dy3+ and Yb3+) results from the substitution of Ln3+ and A+ by a tetravalent cation. The new compound γ-ThEr2F10,H2O (Fm [[3 with combining macron]] m space group, a = 10.739(1) Å and Z = 8) is isotypic with γ-KYb3F10. Water molecules are located inside the tunnels (8c sites) of a CCP stacking of UOA[8] through which they can move. For both series, the thermal stability and the zeolitic behaviour, studied by DTA/TGA and X-ray thermodiffractometry, are reported and a low zeolitic water capacity, around 2–4% in mass, is observed

Spatiotemporal communication with synchronized optical chaos

We propose a model system that allows communication of spatiotemporal information using an optical chaotic carrier waveform. The system is based on broad-area nonlinear optical ring cavities, which exhibit spatiotemporal chaos in a wide parameter range. Message recovery is possible through chaotic synchronization between transmitter and receiver. Numerical simulations demonstrate the feasibility of the proposed scheme, and the benefit of the parallelism of information transfer with optical wavefronts.Comment: 4 pages, 5 figure

Complementarity and Discriminatory Power of Genotype and Otolith Shape in Describing the Fine-Scale Population Structure of an Exploited Fish, the Common Sole of the Eastern English Channel

Marine organisms show population structure at a relatively fine spatial scale, even in open habitats. The tools commonly used to assess subtle patterns of connectivity have diverse levels of resolution and can complement each other to inform on population structure. We assessed and compared the discriminatory power of genetic markers and otolith shape to reveal the population structure on evolutionary and ecological time scales of the common sole (Solea solea), living in the Eastern English Channel (EEC) stock off France and the UK. First, we genotyped fish with Single Nucleotide Polymorphisms to assess population structure at an evolutionary scale. Then, we tested for spatial segregation of the subunits using otolith shape as an integrative tracer of life history. Finally, a supervised machine learning framework was applied to genotypes and otolith phenotypes to probabilistically assign adults to subunits and assess the discriminatory power of each approach. Low but significant genetic differentiation was found among subunits. Moreover, otolith shape appeared to vary spatially, suggesting spatial population structure at fine spatial scale. However, results of the supervised discriminant analyses failed to discriminate among subunits, especially for otolith shape. We suggest that the degree of population segregation may not be strong enough to allow for robust fish assignments. Finally, this study revealed a weak yet existing metapopulation structure of common sole at the fine spatial scale of the EEC based on genotypes and otolith shape, with one subunit being more isolated. Our study argues for the use of complementary tracers to investigate marine population structure

Polarization coupling and pattern selection in a type-II optical parametric oscillator

We study the role of a direct intracavity polarization coupling in the dynamics of transverse pattern formation in type-II optical parametric oscillators. Transverse intensity patterns are predicted from a stability analysis, numerically observed, and described in terms of amplitude equations. Standing wave intensity patterns for the two polarization components of the field arise from the nonlinear competition between two concentric rings of unstable modes in the far field. Close to threshold a wavelength is selected leading to standing waves with the same wavelength for the two polarization components. Far from threshold the competition stabilizes patterns in which two different wavelengths coexist.Comment: 14 figure

Phase-Locked Spatial Domains and Bloch Domain Walls in Type-II Optical Parametric Oscillators

We study the role of transverse spatial degrees of freedom in the dynamics of signal-idler phase locked states in type-II Optical Parametric Oscillators. Phase locking stems from signal-idler polarization coupling which arises if the cavity birefringence and/or dichroism is not matched to the nonlinear crystal birefringence. Spontaneous Bloch domain wall formation is theoretically predicted and numerically studied. Bloch walls connect, by means of a polarization transformation, homogeneous regions of self-phase locked solutions. The parameter range for their existence is analytically found. The polarization properties and the dynamics of walls in one- and two transverse spatial dimensions is explained. Transition from Bloch to Ising walls is characterized, the control parameter being the linear coupling strength. Wall dynamics governs spatiotemporal dynamical states of the system, which include transient curvature driven domain growth, persistent dynamics dominated by spiraling defects for Bloch walls, and labyrinthine pattern formation for Ising walls.Comment: 27 pages, 16 figure

Effects of exogenous dietary advanced glycation end products on the cross-talk mechanisms linking microbiota to metabolic inflammation

Heat-processed diets contain high amounts of advanced glycation end products (AGEs). Here we explore the impact of an AGE-enriched diet on markers of metabolic and inflammatory disorders as well as on gut microbiota composition and plasma proteins glycosylation pattern. C57BL/6 mice were allocated into control diet (CD, n = 15) and AGE-enriched diet (AGE-D, n = 15) for 22 weeks. AGE-D was prepared replacing casein by methylglyoxal hydroimidazolone-modified casein. AGE-D evoked increased insulin and a significant reduction of GIP/GLP-1 incretins and ghrelin plasma levels, altered glucose tolerance, and impaired insulin signaling transduction in the skeletal muscle. Moreover, AGE-D modified the systemic glycosylation profile, as analyzed by lectin microarray, and increased N\u3b5-carboxymethyllysine immunoreactivity and AGEs receptor levels in ileum and submandibular glands. These effects were associated to increased systemic levels of cytokines and impaired gut microbial composition and homeostasis. Significant correlations were recorded between changes in bacterial population and in incretins and inflammatory markers levels. Overall, our data indicates that chronic exposure to dietary AGEs lead to a significant unbalance in incretins axis, markers of metabolic inflammation, and a reshape of both the intestinal microbiota and plasma protein glycosylation profile, suggesting intriguing pathological mechanisms underlying AGEs-induced metabolic derangements

On-chip circularly polarized circular loop antennas utilizing 4H-SiC and GaAs substrates in the Q/V band

This paper presents a comprehensive assessment of the performance of on-chip circularly polarized (CP) circular loop antennas that have been designed and fabricated to operate in the Q/V frequency band. The proposed antenna design incorporates two concentric loops, with the outer loop as the active element and the inner loop enhancing the CP bandwidth. The study utilizes gallium arsenide (GaAs) and silicon carbide (4H-SiC) semiconductor wafer substrates. The measured results highlight the successful achievement of impedance matching at 40 GHz and 44 GHz for the 4H-SiC and GaAs substrates, respectively. Furthermore, both cases yield an axial ratio (AR) of less than 3 dB, with variations in bandwidths and frequency bands contingent upon the dielectric constant of the respective substrate material. Moreover, the outcomes confirm that utilizing 4H-SiC substrates results in a significantly higher radiation efficiency of 95%, owing to lower substrate losses. In pursuit of these findings, a 4-element circularly polarized loop array antenna has been fabricated for operation at 40 GHz, employing a 4H-SiC wafer as a low-loss substrate. The results underscore the antenna’s remarkable performance, exemplified by a broadside gain of approximately 9.7 dBic and a total efficiency of circa 92%. A close agreement has been achieved between simulated and measured results